Related papers: Bad fields with torsion
We give a prescription to add the gravitational field of a global topological defect to a solution of Einstein's equations in an arbitrary number of dimensions. We only demand that the original solution has a O(n) invariance with n greater…
We present a tensor calculus for exceptional generalised geometry. Expressions for connections, torsion and curvature are given a unified formulation for different exceptional groups E_n(n). We then consider "tensor gauge fields" coupled to…
Using a general result of Lusztig, we find the decomposition into irreducibles of certain induced characters of the projective general linear group over a finite field of odd characteristic.
We construct generalised diffeomorphisms for E$_9$ exceptional field theory. The transformations, which like in the E$_8$ case contain constrained local transformations, close when acting on fields. This is the first example of a…
We use the theory of Harbater-Katz-Gabber curves to derive a generalization of the Hasse-Arf theorem for complete local field extensions in positive characteristic.
We provide an up-to-date review of the recent constructive program for field theories of the vector, matrix and tensor type, focusing not on the models themselves but on the mathematical tools used.
We examine the concept of field in tensor-triangular geometry. We gather examples and discuss possible approaches, while highlighting open problems. As the construction of residue tt-fields remains elusive, we instead produce suitable…
We study diffeomorphisms of compact, oriented surfaces, developing methods of distinguishing those which have positive factorizations into Dehn twists from those which satisfy the weaker condition of right veering. We use these to construct…
The existence of a nowhere zero real vector field implies a well-known restriction on a compact manifold. But all manifolds admit nowhere zero complex vector fields. The relation between these observations is clarified.
We present a novel way of constructing the Gaussian Free Field on a weighted graph via a dynamical expansion of the Green function along an expanding family of subgraphs. Along the way we obtain the discrete analogue of the classical…
We consider the application of permutation orbifold constructions towards a new possible understanding of the genus zero property in Monstrous and Generalized Moonshine. We describe a theory of twisted Hecke operators in this setting and…
We use the general theory developed in our article arXiv:1208.5510 in the setting of parabolic geometries to reprove known results on special infinitesimal automorphisms of projective and conformal geometries.
We define and describe the properties of a class of perverse sheaves which is very useful when the base ring is not a field.
In this paper we consider torsion gravity in the case of the Dirac field, and by going into the rest frame we study what happens when a uniform precession as well as a phase are taken into account for the spinor field; we discuss how…
We introduce the notion of differential torsors, which allows the adaptation of constructions from algebraic geometry to differential Galois theory. Using these differential torsors, we set up a general framework for applying patching…
We consider the constraints on the effective Lagrangian of the rank-one gauge field on D-branes imposed by the equivalence between the description by ordinary gauge theory and that by non-commutative gauge theory in the presence of a…
Higher spin tensor gauge fields have natural gauge-invariant field equations written in terms of generalised curvatures, but these are typically of higher than second order in derivatives. We construct geometric second order field equations…
We derive positivity bounds on EFT coefficients in theories where boosts are spontaneously broken. We employ the analytic properties of the retarded Green's function of conserved currents (or of the stress-energy tensor) and assume the…
Incompressible fields are of a special importance in electrodynamics, fluid mechanics, and quantum mechanics. We shall derive a few expressions for such fields in a Riemannian manifold, and show how to generate an incompressible field from…
The structure of integrable field theories in the presence of defects is discussed in terms of boundary functions under the Lagrangian formalism. Explicit examples of bosonic and fermionic theories are considered. In particular, the…